Are you on Trisquel or Trisquel mini? (1) Do you mean actually log off or just lock screen?
(2) These might be of interest https://trisquel.info/en/wiki/play-videos-without-using-flash#toc3
Please be aware of the privacy risks associated with using youtube (=google).(3) Have you tried right clicking the clock applet while holding was it Ctrl (or alt or shift)?
